According to Apple (NSDQ: AAPL), education in the U.S. is plagued both by major institutional problems — low high-school graduation rates, abysmal rankings in science, math and reading — and by inconvenient, heavy and out-of-date print textbooks. The company hopes to remedy those challenges — and tap into the multi-billion-dollar education industry — by partnering with K-12 education publishers on a new iPad textbook initiative, iBooks 2, introduced this morning at an event at New York’s Guggenheim Museum. It is also expanding a revamped iTunes U to K-12 teachers and schools.

In addition, Apple is releasing free software, iBooks Author, which allows users to create any type of interactive e-books — not just textbooks.

Apple’s event today is the first since the death of Steve Jobs in October. According to Walter Isaacson’s biography of Jobs, the former Apple CEO “had his sights set on textbooks as the next business he wanted to transform.” Apple relied on the education market to sustain its Mac business in the 1990s and into the early 2000s, and the company has longtime relationships with buyers in school districts and state education departments, many of whom have switched their focus to iPads. In Q2 2011, Apple sold more iPads than Macs to K-12 education departments.

The iBookstore gets a new textbook category; to start, it includes high-school textbooks from publishers Pearson, McGraw-Hill (NYSE: MHP) and Houghton Mifflin Harcourt as well as some titles from children’s publisher DK and the E.O. Wilson Foundation. The textbooks are all priced at $14.99 or less.

To help publishers further populate the iBookstore with content, Apple is releasing free iBooks Author software, which allows users to create interactive e-books of all types. Users can drag Word files, images, video and widgets — including custom widgets — directly into the program. The books can then be previewed on the iPad and published straight to the iBookstore. “If you’ve ever been involved in any kind of e-book creation project before, you know this is a total miracle in terms of time savings,” said Roger Rosner, VP development, iWork.

Apple’s education announcements today are not limited to K-12 students. The company is also overhauling iTunes U, which it says is used by 1,000 colleges and universities that primarily post lectures. Those lectures have been downloaded over 700 million times since iTunes U’s launch four years ago. The new iTunes U app allows teachers and professors to create complete online courses — with notes, videos, to-do lists, course signups and ratings, etc. The new features seem primarily intended for use within universities, but the iTunes U app will be available to K-12 teachers and schools too.

Numerous startups have focused on digital textbooks, but they are aimed at college students, not elementary- and high-schoolers. In the days leading up to the Apple event, those companies ramped up their own stream of announcements. Textbook rental site Chegg released an e-textbook reading app yesterday, and digital textbook software company Kno said this week that it will add new flashcard and dashboard features to its platform. Meanwhile, iPad textbook publisher Inkling raised $17 million in its most recent funding round and is backed by McGraw-Hill and Pearson (NYSE: PSO). However, none of these companies have emerged as a clear winner in the digital textbook space.

Amazon (NSDQ: AMZN) added Kindle textbook rental in July 2011. Barnes & Noble (NYSE: BKS) sells digital textbooks and offers a little-known e-textbook reading app, Nook Study, for PC and Mac. That app has been available since 2010, and the company has not updated it or paid any attention to it with the subsequent launches of Nook Color and Nook Tablet. (Barnes & Noble’s bricks-and-mortar college bookstores bring the chain substantial revenues — $768 million in Q2 2012, down from $797 million in Q2 2011, “due to a shift from selling new and used textbooks to lower priced, higher margin textbook rentals.”)